A. E. H. Tutton

“ Thus it is clear that in the cases of isomorphous substances, which were the only possible exceptions to the generalisation that to every chemically distinct solid substance of other than perfect cubic symmetry there appertains a specific crystalline form, endowed with its own particular angles and morphological crystal elements, which are absolutely constant for the same temperature, the law does really hold, and isomorphous substances are no exceptions. ”

“ The essence of Mitscherlich’s discovery was, that the chemical nature of the elements present in a compound influences the crystalline form by determining the number and the arrangement of the atoms in the molecule of the compound; so that elements having similar properties, such for instance as barium, strontium, and calcium, or phosphorus and arsenic, combine with other elements to form similarly constituted compounds, both as regards number of atoms and their arrangement in the molecule. ”

“ It is a matter of common knowledge that the mathematical geometrician defines the position of any point in space with reference to three planes, which in the simplest case are all mutually at right angles to each other like the faces of a cube, and which intersect in three rectangular axes a, b, c, the third c being the vertical axis, b the lateral one, and a the front-and-back axis. ”

“ The crystal itself is then our main and highly interesting study; its exterior form unravels itself in a most delightfully simple manner when we follow the arrangement of its faces in zones on the goniometer itself; and its symmetry becomes immediately patent to our eyes in all ordinary simple cases, when we construct for ourselves its plan in a stereographic projection, drawn at first in freehand while still at the goniometer. ”

“ THE SEVEN STYLES OF CRYSTAL ARCHITECTURE. It is truly curious how frequently the perfect number, seven, is endowed with exceptional importance with regard to natural phenomena. The seven orders of spectra, the seven notes of the musical octave, and the seven chemical elements, together with the seven vertical groups to which by their periodic repetition they give rise, of the “period” of Mendeléeff’s classification of the elements, will at once come to mind as cases in point. ”

“ Occasionally a natural biquartz is obtained, on cutting a plate out of a crystal of quartz perpendicularly to the axis. For it is not uncommon to find a crystal which, while apparently a single crystal, is really a twin, the two right and left individuals being joined by an invisible plane of contact, or “plane of composition” as it is called, so beautifully have the two grown together. ”

“ A crystal grows when surrounded by a suitable environment, capable of supporting it with its natural food, namely, its own chemical substance in the liquid or vaporous state or dissolved in a solvent. Moreover, when a crystal is broken, and then surrounded with this proper environment, it grows much more rapidly at the broken part than elsewhere, repairing the damage done in a very short space of time and soon presenting the appearance of a perfect crystal once more. ”

“ Having thus settled what were the units of the crystal structure, Haüy adopted Romé de l’Isle’s idea of a primitive form, not necessarily identical with the molécule intégrante, but in general a parallelepipedon formed by an association of a few molécules intégrantes, the parallelepipedal group being termed a “Molécule Soustractive.” The primary faces of the crystal he then supposed to be produced by the simple regular growth or piling on of molécules intégrantes or soustractives on the primitive form. ”

“ We have thus arrived at morphological constants of very considerable importance, which are best termed “Molecular Distance Ratios,” as they express the relative distances apart in the three directions of space of the centres of gravity or other representative points of contiguous chemical molecules. They are dependent on three experimental determinations, atomic weight, specific gravity, and crystal angles, all of which have now been brought to the highest pitch of refinement and accuracy; hence the molecular distance ratios are particularly trustworthy constants. ”

“ This expansive leap when the molecules of water marshal themselves into the organised order of the homogeneous structure, that of the space-lattice of the trigonal (rhombohedral) system, is one of the most remarkable phenomena in nature, and its exceptional character, so contrary to the usual contraction on solidification of a liquid, is of vital moment to aquatic life. ”

“ If we regard each chemical molecule as represented by a point, disregarding the separate atoms of which it is composed, then these fourteen space-lattices represent the possible arrangements of the molecules in the crystal in all the simpler cases; three of these lattices have cubic symmetry; the tetragonal, hexagonal, trigonal, rhombic and monoclinic systems claim two space-lattices each; while one space-lattice conforms to the lack of symmetry of the triclinic system. ”

“ A form, if of general character, that is, if composed of faces each of which is inclined to all three axes, will comprise more faces the higher the symmetry. Thus, in the cubic system, the form shown in Fig. 21, the hexakis octahedron, comprises as many as forty-eight faces, all covered by the form symbol {321}; while in the rhombic system the highest number of faces in a form is eight, in the monoclinic only four, and in the triclinic system two. It will also have become clear that the law of rational indices limits the number of forms possible of any one type. ”

“ Thus, in spite of the very wise decision of Barlow at the time of developing his theory of the homogeneous partitioning of space, to keep quite clear of attributing shape to the structural unit atoms or molecules, and to consider them as points, he, in common with the other contributors to that splendid geometrical work, appears driven to consider the question of shape when, in collaboration with his chemical colleague, he endeavours to apply his geometrical results to the practical problems of chemistry. ”

“ An interesting and very beautiful lecture experiment was performed by the author in a lecture a few years ago at the Royal Institution, which illustrated in a striking manner this fact that the light reaching the eye from a crystal is of two kinds, namely, white light reflected from the exterior faces and coloured light which has penetrated the crystal substance and emerges refracted and dispersed as spectra. ”

“ When one looks around, and sees the almost complete lack of opportunities for the training of investigators in this rapidly growing branch of science, the importance of which to chemistry and physics is increasing every day, while the field is ripe for the harvesters, one is inclined to feel depressed with the thought of the opportunities which are being lost. ”

“ When a plate of either quartz or calcite one-fiftieth of an inch thick, cut perpendicularly to the optic axis, is examined under the polariscope or polarising microscope, the dark field is unaffected by its introduction on the stage, remaining dark on a complete rotation of the crystal plate in its own plane. Moreover, the calcite plate continues to behave similarly however much the thickness is increased, the field remaining dark. But when quartz is examined as regards the effect of thickness an extraordinary thing happens. ”

“ EFFECT OF THE SYMMETRY OF CRYSTALS ON THE PASSAGE OF LIGHT THROUGH THEM. QUARTZ, CALCITE, AND GYPSUM AS EXAMPLES. The action of transparent crystals on the rays of light which they transmit is a subject not only of the deepest interest, but also of the utmost importance. For it is immediately possible to detect a cubic crystal, and to discriminate between two groups, optically uniaxial and biaxial respectively, of the other six systems of symmetry, three systems going to each group, by this means alone. For a cubic crystal is singly refractive in all directions. ”